Allocating Transit Costs and Revenues

This post arises from a discussion at Toronto Council’s budget debates in which the question of the profitability of various parts of the system came up. This triggered a Twitter thread in which I eventually said “2 big 4 tweets”, and offered to write about this issue here.

Please note that this discussion will be theoretical, not a specific examination of TTC or any other system’s costs because (a) I don’t have the raw data, and (b) the level of analysis needed to ferret out the level of info needed is something requiring inside knowledge of each agency’s accounting practices.

In effect, this article is a caveat: anyone who tells you they can produce a profit and loss statement on a line-by-line basis in a system where fares and costs cannot be accurately subdivided between system components is, to be gentle, full of hot air. Politicians and bureaucrats love metrics, numbers that purport to allow comparison between portions of a system, between cities, etc, in the elusive search for a “more efficient” operation. They have wet dreams about metrics that can reduce a complex universe to a single dimensional value with a “traffic light” to indicate current status.

This misses the point that “value” can be a subjective measurement depending on your goals. For example, an 80% farebox cost recovery number is boy-scout-badge-worthy if your goal is to provide the most service at the lowest net cost, but it could mask the rejection of any new services that would not contribute to the target level of recovery. Services that might be desirable for other benefits such as time of day or geographic coverage could be rejected because they will spoil the overall system numbers. Moreover, a metric might have a different target depending on the type of service it measures — we expect far more from a subway line because of its high capital cost than we do from a local bus route.

Cost Allocation

The Operating Budget covers the day-to-day cost of providing service and managing the system. Within this, costs can be subdivided by mode (to the extent that they are incurred by each fleet and type of infrastructure within the system), with a left over component for general management.

Once upon a time, transit systems including the TTC boiled all of this down to a cost per vehicle mile. This is a very misleading value because the lion’s share of costs do not actually vary with the distance a vehicle travels, but rather with the amount it is used, typically expressed in vehicle hours. On a system where most routes run at similar speeds, miles and hours are interchangeable, but if there are wide variations, distortions in the quoted cost arise.

The simplest example is the cost of the driver which is roughly the same for all modes (I will explain “roughly” later). Drivers are paid in hours, not miles, and if they are on a slow streetcar or bus route their cost per vehicle mile is higher than on a fast suburban route. This is not an inherent advantage of buses, but of where they are used. Similarly, the crew on a subway line with widely spaced stations will cost “less” per train mile than a crew on the older part of the system with stations close together and heavy demand that adds to dwell time.

I said “roughly” above because some distortion is introduced in allocated costs by the relative popularity of transit modes among operators. The proportion of lower-paid junior operators may vary by mode depending on the relative popularity of parts of the system, and so the actual hourly rate paid for a bus driver hour may not be the same as for a streetcar driver hour. Other factors that can come in are the ratio of driving time plus various allowances to actual in service time. If vehicles spends a lot of time going to and from the garage (a rush hour tripper for example), the cost per hour of service provided is higher than a route where most vehicles stay in service throughout the day.

Fleet and infrastructure contribute a lot to costs, but this too can be distorted. Some types of maintenance are performed on a calendar cycle, the simplest being a daily cleaning (leaving aside the question of whether this actually occurs for some of the TTC’s fleet). It does not matter whether a bus does a few trips in the rush hour on a slow route, or is out all day on a fast one, it requires some basic cleaning and servicing at the garage. Buses run on faster routes, accumulate more mileage per day, and so dilute the fixed costs relative to streetcars running on slower routes. The fact that buses running on streetcar routes would be at least as slow is often missed in mode-to-mode comparisons. (This is a matter of record for routes the TTC has converted.)

Some costs are more-or-less fixed and will be incurred regardless of how much service is operated. This includes facilities costs (buildings, yards, tunnels, stations), the cost of station operations (power, elevating device maintenance, station staffing, ventillation, etc) and the cost of a the small army of standby mechanics and technicians who are available to fix whatever breaks on a timely basis.

Each of these will include varying proportions of labour costs (materials and utilities are other major areas), and overheads such as benefits apply only to the labour component.

Finally, there is the overhead of system management that is generally not sensitive to the scale of operations unless there is a very large addition to or removal of service.

Costs for new services (or the savings from removing existing services) should be calculated on a marginal basis based on the actual amount of resources in each category that are added or removed by the change.

When the TTC reports the daily cost of a route’s operation, this is based on almost entirely on vehicle hours, vehicle miles and peak vehicles. It is very important to note that there is no charge against operations for capital. This can distort ongoing costs for modes, notably the subway, where a substantial amount of ongoing “maintenance” is capitalized and therefore not included in the operating cost base. Furthermore, even though interest on capital debt is properly an “operating” expense, it is charged to the City’s accounts (for debt raised on the TTC’s behalf), not to the TTC’s accounts (where it would have to be offset by a subsidy or by higher fares).

The TTC does not now report daily operating costs for its rapid transit modes, only for the surface routes.

(This is a “costing 101” overview to which much more detail could be added, but for the purpose of this discussion, those are the main points.)

Allocating Revenue

Let me start by saying that this is almost impossible, especially for the TTC’s fare structure. I will review various attempts that have been made to allocate revenues and why each scheme produces distortions in reported results.

First a very simple counter example from another system, GO Transit.

Fares on GO are charged, loosely speaking, by distance although there are systemic biases in these values with shorter trips charged a higher cost per kilometre travelled. Leaving a discussion of whether that is “fair” to riders aside, the basic point is that each leg of a GO journey attracts its own fare, and therefore the revenue can be directly allocated to the service that “earns” it.

As GO Transit’s service pattern and integration with other networks becomes complex, the allocation of GO fare revenue will become trickier even if trips are tracked in detail via the Presto system. The reasons will be clear when we look at TTC fares.

A TTC rider either:

pays a cash fare

uses a ticket or token

swipes/waves a daily, weekly or monthly pass

In the first two cases, counting fares is easy, and in the case of passes, the TTC (through surveys) learns what the average usage of each type of pass is and converts this back to “trips”. Discussions of pass pricing always turn on whether the discount given to riders who get a lower fare per trip is justified in some cosmic sense of “fairness” in revenue generation. The most recent fare increase included a bump in adult Metropass pricing to compensate for alleged increase in pass usage and the premise that passholders are employed and “could afford it”.

One way or another, the TTC boils all of its income and fare media used down to a count of trips, and hence an average fare. It is not clear whether this is valid across the entire system (do more riders pay by pass on downtown routes than in the suburbs, for example), but the assumption is that each trip generates the same average revenue.

When TTC management were first asked to produce profitability statements for routes, they had to come up with a way to allocate fares and the scheme was based on distance travelled. Here is how it worked:

It is possible to calculate an average trip length from travel survey data, and it works out that a TTC “trip” is, on average, around 8-9km.

Divide the average fare by, say, 8.5 to get a revenue per km travelled.

The average occupancy of vehicles on a route can be calculated from detailed riding counts. If a bus has an average load of 10 and the bus travels 100km, then this represents 1,000 passenger km.

Revenue was allocated to routes based on the estimated amount of travel on them.

There were a few major problems with this scheme, of which the most basic is that a very long trip will allocate far more revenue to the routes it uses than the rider actually pays. A very short trip will allocate far less. This distorted revenue allocations toward routes that served long trip segments.

The second attempt tried to correct for part of the problem by estimating the proportion of “one seat rides” each route used. For example, if half of the riders on the King car made trips from one point to another on that route, they would allocate a full fare to the route regardless of the trip length. Revenue for all remaining trips was allocated as in the original scheme.

This arrangement still didn’t work very well and perpetuated the problem that long trips would allocate much more revenue overall (and thereby make the affected routes more profitable on paper) than short trips, unless no transfer was involved.

The third scheme got rid of distance (a complicated number to deal with anyhow) and shifted to “boardings”. Transit trips consists of many “links”, individual sub-trips taken on one or more routes that together make up one journey. Fare revenue is allocated per boarding, although the subway network is considered one “boarding” even though a transfer move might be involved. In practice, the average number of boardings per trip for TTC riders is about 2 — the average rider transfers once in a journey. Obviously some don’t transfer at all, and others transfer more than once.

Again this system distorts revenue allocation because a one-seat ride will only allocate half a fare, while a three-seat ride will allocate 1.5 fares. Again, long trips (which are more likely to include multiple transfers) overallocate fare revenue while short trips underallocate. This can be partly compensated for via the “one seat ride” adjustment described above, but that was not done in practice, and it still does not really fix the problem.

Because the amount of revenue allocated has nothing to do with the amount of service consumed on a route (a trip for one stop allocates the same as a trip halfway across town), this produces a peculiar effect. Short routes always make a profit. The reason for this is that long trips are impossible, and so the allocated revenue relative to the service consumed is always high. Routes like Main, Wellesley and Coxwell always did spectacularly well by this measure, although it did not encourage the TTC to improve service on them. (These routes also have strong demands both ways, and in some cases, multiple major destinations with their own local traffic along the route.)

For the sake of argument, assume that we knew the complete details of everyone’s transit trip through a smart card. Should we allocate revenue based on distance travelled or time used? In each case we are not even dealing with the same fare value depending on the type of fare a rider is using. Should pass revenue be distributed over a month’s usage, or allocated based on an “average” value for all pass use?

Presuming that such a scheme were practical, it would have the reverse effect of earlier allocations in that long trips would contribute much less revenue per unit of service consumed, and it would be impossible for trips with multiple links to overallocate revenue. This would have a profound effect on the “profitability” of routes serving those long trips, and yet it is precisely this type of trip where private autos give the TTC the most competition. As a matter of public policy, should we be encouraging long transit rides through the subsidy mechanism of a flat fare? Should service levels be based on encouraging riding, even at a loss, through convenience and lower crowding levels? If there is a “loss”, what are we buying for that expenditure?

Major System Changes

In cases where there is a large-scale change in the system such as opening a new subway line (and reorganizing feeder routes), or changing service standards to increase or decrease the acceptable load on vehicles, the change in operating costs is big enough that it can be calculated for the system as a whole.

For example, when the Sheppard Subway opened, the cost of operating and maintaining the subway was a net new cost, and the reorganized bus network had gains and losses from discontinued parallel services and the addition or improvement of feeder routes. Some new riding generated offsetting revenue. At the time, it was estimated that the net cost per ride on that line was about $10. This number has fallen as riding improved, but is likely still well above the cost/ride on other parts of the subway system.

The problem we have, however, is that Sheppard is now an integrated part of the whole, and we cannot recoup those costs simply by running fewer trains, or even closing the line. A similar problem faces the TTC when the Spadina extension opens to Vaughan in 2016. The cost of doing business will go up disproportionately to the additional revenue. Many riders will simply be redirected from existing TTC services, but will get a higher quality of service on the new subway. The projected number of new TTC riders will not generate enough new fare revenue to offset the subway’s operating cost.

As subways age, they start to incur major maintenance costs. Some of these affect the operating budget (routine fix-ups) and some affect capital. Therefore, in the short term, the marginal cost of a new subway is understated. Opening day and life-cycle costs are not the same.

Changes in service standards trigger effects in two areas. One is the cost (or saving) from service added or removed (or the avoided cost of a service increase where more riders are stuffed onto the same buses). The other is from capital costs in the need for a given fleet size to serve a given demand across the system. This can show up as one-time savings in the year in which service standards get worse, but this is not repeatable once all of the “extra” space has been tuned out of the service.

Conclusion

Trying to estimate the “profitability” of any part of the system is a game for politicians (and sycophantic bureaucrats) who cannot get beyond a nose-in-the-books attitude to the provision of public service. The real questions are “are people riding the system” and “do we provide service at a level that is attractive across the network”.

As I discussed here, it is almost impossible to create an allocation system that will accurately reflect how any one part of the system behaves. Moreover, just because the Yonge line might be wildly profitable, we cannot simply chop off services that don’t do as well (or, worse, contemplate giving the most “profitable” pieces to another agency) because each route, each segment is part of a network and contributes to the overall system.

Exercises in cost and revenue accounting lead us down a blind alley where we will get meaningless numbers and bad policy decisions.

This is not to say that we should provide service without caring about the cost — at some point the demand is too low to justify using buses for a handful of riders. That said, there is more to do both in terms of managing the service that is operated, and providing resources to improve service capacity and quality to retain and attract riders.

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9 thoughts on “Allocating Transit Costs and Revenues”

In conclusion, the TTC is forced to make many assumptions to not only allocate costs & revenue by mode & route; but also in its calculation of daily rides (TTC Armed Revenue Staff in armored cars collect the “fare boxes” from each bus, streetcar, RT station each night, after close, transports them to secure facility where staff dump them out on a conveyor belt & count the cash, tickets, tokens they contain. These daily (or sometimes weekend receipts) are then sent to HO where Finance Staff analyze them and using a huge dollop of experience & judgment calculate the daily rides (after applying trip multiples derived from a periodic surveys (Day, Weekly, GTA Weekly passes) or a small number of monthly diary panels for MP (Adult, Senior, SStudent, UStudent, VIP, MDP{A,S,S,SS,US}, Bulk…), a sample size that is too small to attribute different rides to each MP class (so more TTC judgment is applied).

So any rev/ride, any costs/ride as well as same for individual routes & modes incur double jeopardy in that the TTC doesn’t actually have a real total count or realtime data to determine the revenue, costs, or rides on a daily basis (and therefore weekly, monthly & annual basis as well) so any calculation of them has a much greater margin of error than the TTC admits to.

For example, TTC Executives when queried, tell the Commission “Our counts” show our ride forecasts are very accurate, within 1%). That’s patently absurd — that 22 “Checkers” in Service Planning who periodically audit or count a route, subway or station (sometimes counts are years old) can possibly represent the dynamics & variations in daily rides across a city plagued by frequent & constantly changing congestion & delays. It’s presently impossible for the TTC to do a daily system-wide “count” with just 22 checkers tasked with simultaneously counting rides on 2,804 vehicles on 152 routes with 69 RT stations with multiple entrances.

I have yet to hear a Commissioner question the veracity of Staff’s 1% ridership accuracy claim, they simply don’t have the experience, expertise, knowledge or confidence to rock the boat and challenge Staff. They don’t realize just how manual, how judgmental the TTC projections are, and will continue to be until real time data is finally available to them.

The PRESTOcard, second generation should have the on chip memory to provide tap-on data that will finally give the TTC the real time data that will allow them to fine-tune service to where the ride demand is, not in 10 board periods, but weekly, daily, even hourly. The revenue, cost, rides and allocations will then be much more accurate than is possible in today’s manual count/calculation system.

A minor quibble on “1. Pays a Cash fare. …counting fares is easy”

It’s easy to count TOTAL cash, but, judgment still has to be exercised by TTC Staff to break the total cash number into rides by: Adults ($3.00), Seniors ($2.00), Students ($2.00), Child (75¢). I’m not sure how the TTC handles accounting of cash used to pay for other fare media (eg. MP, S/S tickets, tokens, DayPass, etc.)

Steve: With vehicles equipped with automatic passenger counters, getting detailed riding counts does not depend only on the service checkers. The real challenge for farebox based counts is that it does not include the over 50% of trips that do not pay a fare on board (passes, transfers). Overall ridership can be calculated from revenue, but route level counts need on board details either from checkers or APCs.

Steve: Even for you this is a remarkably thoughtful and informative posting. Thank you. Perhaps you should send a copy to all Commissioners and all Councillors?

Steve: Some days I can be very mellow. The Commissioners and Councillors who care already read my blog (or their staff do to flag interesting bits). The rest would consider this well beyond their attention span.

You should have heard the debate about timed fares at the Commission meeting where it was clear that some members of the Board did not have the faintest idea of how fares work now or would work in the future.

… anyone who tells you they can produce a profit and loss statement on a line-by-line basis in a system where fares and costs cannot be accurately subdivided between system components is, to be gentle, full of hot air.

Your kind flavour of diplomacy made me smile – we all understand what they are really full of. 😉

Steve: Oxford English Dictionary, Complete Edition. One who goes on a trip, or short journey. By extension, a “tripper” is a car (or route) that operates limited service, typically in the peak, on a different route from the regular service. See “503 Kingston Road Tripper”.

Steve, isn’t part of the problem with travel time, distance, etc. that commuters may not use one bus or streetcar to get from Point A to Point B? This can make it more difficult to apply revenue (the fare the person paid) to the cover costs, as there may be several routes involved.

Steve: That’s the nub of the problem. Multiple routes/vehicles are involved in a trip. If total system revenue is allocated either by distance or time consumed, or by number of vehicles, this will always over-allocate for longer trips with multiple transfers and under-allocate for everything else. If trips were actually tracked individually and there were some way to allocate the actual revenue among the trip segments, then routes that serve long trips will suddenly not be as “profitable” as they were under the other schemes.

What is far more basic is the actual usage of a route — how much travel is the TTC serving by operating “x” amount of bus or streetcar hours. Policy factors such as maximum headways and allowable low loads may preserve some not very productive services, but that’s what the policies are all about.

As a professional Accountant, this is not only my area of expertise, but I find it quite fascinating. In theory, one can set up a theoretical model for allocating costs and revenues in the TTC. But actually implementing this model is very, very difficult.

So, here goes with the theory for allocation revenues.

The way to allocate revenues is to look at all of the social benefits produced by the TTC, as well as any possible disbenefits or harms. Then we weight each benefit by its social utility. Next we analyse how each TTC operation generates these benefits. Finally, we allocate revenue accordingly.

This is, of course, much easier to write than it is to do. Let me give a few examples.

How do we weight the value of a short trip vs. a long one? Perhaps a trip should be valued with a fixed per trip revenue plus a variable distance-based allocated revenue.

Do we give a higher value for a trip that was practical for the passenger to use an automobile instead? Perhaps we should invest more in operations where we are luring people out of cars and less in operations where passengers are essentially a captive market with little competition.

One example of a social benefit is providing transportation for disabled persons. In allocating revenue, should we put a higher weight upon a trip taken by a disabled person?

The current paradigm of disability accommodation is an engineering one based upon minimum standards. How do we decide when demand is high enough to exceed those standards? For example, in our cost/benefit analysis, what level of demand justifies the cost of a second elevator in a high-demand location? How do we weight other users of the elevator such as cyclists or parents with baby strollers? Does the disabled user “count more” in deciding if there is enough demand to cost justify that second elevator?

Revenues need to be matched to the social benefits generated by TTC operations in order to do a proper cost/benefit analysis for proposed spending. And these are the sort of questions that need to be asked when allocating revenues. There are no easy answers to these questions, but this is the approach that should be taken when deciding how to invest our limited resources.

Otherwise… sigh… we have only raw politics and who can scream the loudest for what they want. Which, most unfortunately, is how far too much of our limited resources have been misallocated.

Steve: As I said in a previous reply, all of this accounting is a nice exercise (you can probably tell that I have been wrestling with it for years), but the important question is whether service is actually being used and what benefit the service provides. We can get so hung up on the cost and revenue accounting that we forget that the job of the TTC is to move people. Some of that work is easy and cheap to do, other trips consume a lot of resources. The policies on the quality of service we want to provide should come first, not an abstract and almost certainly flawed accounting exercise.

We can definitely cost things like the marginal cost or saving of some change such as setting a maximum headway of 20 minutes, or revising loading standards to reduce crowding. But those are system level costs that are the accumulation of effects on many routes, and the delta is big enough to (a) calculate and (b) be part of a meaningful policy decision. Things fall apart at the individual route level where the degree to which service is used (including questions about why it isn’t used more) should take precedence.

The PRESTOcard, second generation should have the on chip memory to provide tap-on data that will finally give the TTC the real time data that will allow them to fine-tune service to where the ride demand is, not in 10 board periods, but weekly, daily, even hourly. The revenue, cost, rides and allocations will then be much more accurate than is possible in today’s manual count/calculation system.

The data will be a fine thing to have … and the accuracy improvements will be great … but it reminds me of a little routine my son and I have when reading. At a particularly interesting point in the story, before I turn the page I always “what do you think happens?” if the story is new or “and then what happens?” if he’s familiar with it. His response for the second is always “uh oh!”

So I feel like I’ve heard the story before … with GPS-tracking of buses. Lots of data but TTC doesn’t appear to be doing much with it to improve the level of service and dealing with line management issues. As far as I can tell the only thing the TTC appears to be doing with those data (at the moment) is paying them over to Steve for his analysis and nothing more. (Uh oh!)

I don’t even know if they are using his analysis of those data for anything constructive. (Uh oh! again) Now to be fair to the TTC if they are doing anything please let us know about it and I’ll be the first to stand corrected.

In the meantime … Steve, do you think it will be long before you are analyzing Presto Card data passed over to you by the TTC?

Cheers, Moaz

Steve: Actually, the TTC is now doing some analyses of its own using the GPS data, but I don’t know if it is as extensive as my work. I have been repeatedly asked about meeting with TTC staff, but they never, ever get around to actually organizing such a get together. The background article explaining how my processes work was written explicitly to give the folks who are doing the work some insight into my own methods in lieu of us actually getting together.

I have a lot of unpublished analyses, but don’t have (nor do I ask for) anywhere near 100% of the system. That would be a huge set of data just for one month, and frankly, I am only interested in a few major routes as examples of general, repeatable behaviour patterns and longitudinal tracking. Some day, I want to push more of these out of the door, but there are other transit issues to cover, and my own life has a lot more to it than writing about transit.

Presto data? No thanks. The volume would be enormous, and I actually do not want the TTC to implement a system where they can track every trip beginning to end (i.e. tap in and out for all trip segments). This is passenger inconvenience in the name of a management tool hardly anyone will ever use. The TTC has buses (and eventually streetcars) with automatic passenger counters, and these can be deployed on various routes as needed to get counts. Presto has nothing to do with this capability, and passenger tracking has been used as a “sales pitch” by Presto vendors to people who should know better.

Yes, with Presto you can get the linked trips rather than simply the usage at individual points, but do you honestly expect the TTC will restructure its system around travel patterns? The routes generally form a grid for a reason.

Even if we can allocate the exact cost through the use of IC cards, it would still be a pointless exercise. Most of the TTC rides originate from a bus or tram service and then feed to the metro system. Without the feed from buses, the metro system would probably not be as well used. Buses have the highest cost per seat mile and additional seat miles. But the metro network is already a sunk cost and it costs money just to maintain (like tunnel liners) whether it is one passenger or a billion passengers. It makes sense for the TTC to use the bus network to feed passengers at a substantial cost.

A return ticket from YYZ to YHZ costs about $600 in Y on Air Canada. Yet, for a trip from YYZ to NRT, it costs only about $1150. From YHZ to NRT via YYZ only cost $1271. This is about a $120 difference versus buying the ticket separately. AC sells the tag on at less than cost price just to attract a customer to fly on their trunk route. Keep in mind that the cost per seat mile on the YHZ to YYZ leg costs substantially more than the YYZ to NRT leg due to the use of regional jets.

If that passenger books a flight with UA or AA, it is lost revenue for AC. Large planes like the Boeing 777-300ER needs to be filled to be profitable. Like the TTC’s metro, AC cannot simply not fly to NRT because it is unprofitable. They will lose the slot if they do not fly there. Likewise, the TTC for whatever reason needs to run its metro system from 5AM to past midnight in six car trainsets at every five minutes. Then it should be prepared to subsidized the feeders to feed it. Does that mean routes like 167 should be scale back because it is unprofitable? No, without it, there will be less passengers at Warden Station using the metro.

Similar issues apply with any transportation network. The arguments over Amtrak’s accounting have gone on for four decades, and are no closer to a “conclusion”.

The “change in the bottom line” from deleting a route or adding a route is possible to estimate, more or less. But you can’t just list these out and add them up, because there are synergies (economies of scale, network effects) between routes.

Add route A and your bottom line gets worse by $X; add route B and your bottom line gets worse by $Y; but add both route A and route B and suddenly your bottom line get *better* by $Z.

This sort of stuff happens all the time in transportation networks (and probably communications networks too). You have to look at them holistically to get meaningful results.